# A triangle has sides A,B, and C. If the angle between sides A and B is #(3pi)/8#, the angle between sides B and C is #pi/4#, and the length of B is 7, what is the area of the triangle?

##### 1 Answer

≈ 17.32 square units

#### Explanation:

The area of a triangle can be calculated using

#1/2ab sintheta#

where#theta" is the angle between a and b "# In this triangle , only know the length of one side B. Require to find the length of A or C.

This can be done using the

#color(blue)" sine rule "#

#A/sinA = B/sinB = C/sinC #

where the angles A , B and C on the denominator represent the angles opposite the corresponding sides A , B and C.

#color(red)" Calculating the length of side C" # using

# B/sinB = C/sinC# Before using this, require the size of angle B

The sum of the 3 angles in a triangle

# = pi# angle B

#= [pi - ((3pi)/8 + pi/4 )] = pi - (5pi)/8 = (3pi)/8# Now angle B = angle C hence side B = sideC = 7

In this question B = C = 7 and

#theta = pi/4#

#"area" = 1/2xxBxxCsintheta = 1/2xx7xx7xxsin(pi/4) ≈ 17.32#